Settings (9-16) are based on the disentanglement framework we present. In these settings ,\(\mathcal {L}_{recon}\)  and \(\mathcal {L}_{adv}\)  are used throughout. Using only the reconstruction (\(\mathcal {L}_{recon}\) ) loss and adversarial loss (\(\mathcal {L}_{adv}\) ) in (9), which is the baseline method of [1]}, the sensitive accuracy is \(58\%\)  and the label prediction is \(60\%\) , which shows that disentanglement improves upon the baseline classifier. Compared to the adversarial setting of (2), it classifies the sensitive attributes more accurately (worse) but also classifies the true test labels \(y\)  more accurately (better).
Adding a small portion of \(\mathcal {L}_{y}\)  in (10), by using \(\lambda _3 = 0.1\) , leaves the results the same.
However, the significant gain is achieved by adding to (9) the local fairness loss (\(\mathcal {L}_{local}\) ) as shown in (11). Here, the accuracy of the sensitive variable is reduced by \(5\%\)  to \(53\%\) , while leaving the label prediction rate the same.
Finally, considering, the full loss \(\mathcal {L}_{full}\)  by using \(\lambda _1 = 1\) , \(\lambda _2 = 1\) , \(\lambda _3 = 0.1\)  in (12), achieves the best results with sensitive accuracy of \(53\%\)  and true labels \(y\)  accuracy of \(61\%\) . Overall, we observe that local fairness improves accuracy, but only in the case where a disentangled representation is used.
